Career Choice and Academic Performance

Chris Cioffi, Kristina Frazier, Aidan Hennessy, Mike McHenry

Overview

  1. Introduction and Question
  2. Background and Related Literature
  3. Data
  4. Exploratory Analysis
  5. Modeling
  6. Diagnostic Tools
  7. Remedial Measures
  8. Conclusion

What Do You Want to Be When You Grow Up?

  • During high school, young adults are often asked to make decisions regarding post-secondary education that can have a profound and lasting impact on their lives in the future.

  • We investigate what factors in high school may be related to future academic performance.

Research Question

  • Question: How is college GPA related to prospective career path in high school? How are other characteristics about a student’s background and high school environment related to their college GPA?

  • This study aims to investigate whether students who have a desired future career path in the 9th grade perform better than students who do not, and if choice of career path matters.

Data

  • High School Longitudinal Study of 2009 (HSLS:09) from the National Center for Education Statistics.
    • Interviewed 9th graders across the United States in 2009.
    • Followed up with subjects in three subsequent interview rounds.
    • Offers a variety of information on students, parents, and school.

Key Variables

  • Response Variable: College GPA

  • Primary Predictor of Interest: Desired occupation at age 30.

    • A categorical variable with 22 occupation groups.
  • Additional predictors:

    • Academic: High school GPA, credits earned for AP/IB courses, School engagement, Stem/non-stem desired occupation
    • Geographic and Socioeconomic Factors: Family Income, High School urbanicity, High School type

A Look at Desired Occupation

Desired Occupation and Academic Performance

Color-coded by Planned student occupation at age 30

            College_GPA    HS_GPA
College_GPA   1.0000000 0.5630064
HS_GPA        0.5630064 1.0000000

Model: Simple Linear Regression

  • Set reference group to those students who answered “Don’t Know”.

  • Model takes the form of \(College\_GPA = \beta_0 + \beta_1future\_job + \epsilon\).

Results: Simple Linear Regression

  • Showing only results with a p-value < 0.10.
# A tibble: 7 × 5
  term                                      estimate std.error statistic p.value
  <chr>                                        <dbl>     <dbl>     <dbl>   <dbl>
1 (Intercept)                                  2.72     0.0170    160.   0      
2 Education, Training, and Library Occupat…    0.192    0.0454      4.24 2.28e-5
3 Arts, Design, Entertainment, Sports, and…   -0.109    0.0303     -3.60 3.16e-4
4 Protective Service Occupations              -0.317    0.0595     -5.33 1.00e-7
5 Food Preparation and Serving Related Occ…   -0.329    0.0878     -3.75 1.79e-4
6 Installation, Maintenance, and Repair Oc…   -0.271    0.104      -2.62 8.84e-3
7 Military Specific Occupations               -0.358    0.0725     -4.94 8.08e-7
  • Adjusted \(R^2\) is less than 1%.

Additional Variables

Additional Variables

Additional Variables

Additional Variables

Multiple Linear Regression

Initial MLR Model: \[College\_GPA = \\ \beta_0 + \beta_1future\_job + \beta_2college\_gpa + \beta_3major\_considering + \\ \beta_4family\_income + \beta_5credits + \beta_6school\_type + \beta_7urbanicity + \\ \beta_8school\_belonging + \epsilon\]

  • Adjusted \(R^2\): 0.3563
  • F-statistic: 66.59 on 62 and 7286 DF, p-value: < 2.2e-16

Remove Urbanicity & School Belonging?

  • Urbanicity: Betas for all 4 categories (City, Rural, Suburb, & Town) are insignificant at alpha = 0.10
  • School Belonging: P-value for beta is 0.80

Lack of Fit Test

  • Null Hypothesis: \(\beta_7urbanicity\) = \(\beta_8school\_belonging\) = 0

  • Alternative hypothesis: either of the betas for these variables is a non-zero value

  • Use alpha = 0.10

Remove Urbanicity & School Belonging?

Analysis of Variance Table

Model 1: X5GPAALL ~ X1STU30OCC2 + X3TGPAACAD + X4ENTRYMAJ23 + X1FAMINCOME + 
    X3TCREDAPIB + X1CONTROL
Model 2: X5GPAALL ~ X1STU30OCC2 + X3TGPAACAD + X4ENTRYMAJ23 + X1LOCALE + 
    X1FAMINCOME + X3TCREDAPIB + X1CONTROL + X1SCHOOLBEL
  Res.Df    RSS Df Sum of Sq    F Pr(>F)
1   7290 3608.0                         
2   7286 3605.7  4    2.2764 1.15  0.331
  • With a P-value of 0.331, there is insufficient evidence to reject the null hypothesis that the values for the betas of these two predictors are not zero.

  • The lack of significant relationship between Urbanicity & School Belonging was seen in earlier plots.

Variable Selection

New MLR Model: \[College\_GPA = \\ \beta_0 + \beta_1future\_job + \beta_2college\_gpa + \beta_3major\_considering + \\ \beta_4family\_income + \beta_5credits + \beta_6school\_type + \epsilon\]

  • Stepwise selection did not remove additional variables

Diagnostics

Linearity

  • F-statistic: 71.1 on 58 and 7290 DF, p-value: < 2.2e-16

Call:
lm(formula = X5GPAALL ~ X1STU30OCC2 + X3TGPAACAD + X4ENTRYMAJ23 + 
    X1FAMINCOME + X3TCREDAPIB + X1CONTROL, data = MLR_all)

Residuals:
     Min       1Q   Median       3Q      Max 
-3.11365 -0.34477  0.09234  0.43827  2.75491 

Coefficients:
                                                                        Estimate
(Intercept)                                                            0.4541565
X1STU30OCC2Management Occupations                                      0.0153304
X1STU30OCC2Business and Financial Operations Occupations               0.0782835
X1STU30OCC2Computer and Mathematical Occupations                      -0.0370277
X1STU30OCC2Architecture and Engineering Occupations                   -0.0585375
X1STU30OCC2Life, Physical, and Social Science Occupations             -0.0304988
X1STU30OCC2Community and Social Services Occupations                   0.1392815
X1STU30OCC2Legal Occupations                                          -0.0737682
X1STU30OCC2Education, Training, and Library Occupations                0.0670447
X1STU30OCC2Arts, Design, Entertainment, Sports, and Media Occupations -0.0050668
X1STU30OCC2Healthcare Practitioners and Technical Occupations         -0.0302980
X1STU30OCC2Healthcare Support Occupations                              0.0869059
X1STU30OCC2Protective Service Occupations                             -0.0524724
X1STU30OCC2Food Preparation and Serving Related Occupations           -0.2356375
X1STU30OCC2Personal Care and Service Occupations                       0.0982343
X1STU30OCC2Sales and Related Occupations                               0.0434307
X1STU30OCC2Farming, Fishing, and Forestry Occupations                  0.1171752
X1STU30OCC2Construction and Extraction Occupations                     0.0705477
X1STU30OCC2Installation, Maintenance, and Repair Occupations           0.1269173
X1STU30OCC2Production Occupations                                      0.1494096
X1STU30OCC2Transportation and Material Moving Occupations              0.1271622
X1STU30OCC2Military Specific Occupations                              -0.1665261
X3TGPAACAD                                                             0.6807046
X4ENTRYMAJ23Computer and information sciences                         -0.0041207
X4ENTRYMAJ23Engineering and engineering technology                     0.0002693
X4ENTRYMAJ23Biological and physical science, science tech              0.0805061
X4ENTRYMAJ23Mathematics                                                0.0729173
X4ENTRYMAJ23Agriculture and natural resources                          0.1474664
X4ENTRYMAJ23General studies and other                                  0.1499260
X4ENTRYMAJ23Social sciences                                            0.1688093
X4ENTRYMAJ23Psychology                                                 0.1377309
X4ENTRYMAJ23Humanities                                                 0.2607402
X4ENTRYMAJ23History                                                    0.1475859
X4ENTRYMAJ23Personal and consumer services                             0.1386387
X4ENTRYMAJ23Manufacturing, construction, repair, transportation        0.4337423
X4ENTRYMAJ23Military technology and protective services                0.1482326
X4ENTRYMAJ23Health care fields                                         0.1591009
X4ENTRYMAJ23Business                                                   0.1194903
X4ENTRYMAJ23Education                                                  0.2294671
X4ENTRYMAJ23Architecture                                               0.2198331
X4ENTRYMAJ23Communications                                             0.2830411
X4ENTRYMAJ23Public administration and human services                   0.1670796
X4ENTRYMAJ23Design and applied arts                                    0.2517047
X4ENTRYMAJ23Law and legal studies                                      0.2328264
X4ENTRYMAJ23Theology and religious vocations                           0.3499678
X1FAMINCOMEFamily income > $15,000 and <= $35,000                      0.0097161
X1FAMINCOMEFamily income > $35,000 and <= $55,000                      0.0542806
X1FAMINCOMEFamily income > $55,000 and <= $75,000                      0.1061207
X1FAMINCOMEFamily income > $75,000 and <= $95,000                      0.0811145
X1FAMINCOMEFamily income > $95,000 and <= $115,000                     0.1507057
X1FAMINCOMEFamily income > $115,000 and <= $135,000                    0.1707281
X1FAMINCOMEFamily income > $135,000 and <= $155,000                    0.1262002
X1FAMINCOMEFamily income > $155,000 and <=$175,000                     0.0952562
X1FAMINCOMEFamily income > $175,000 and <= $195,000                    0.1803418
X1FAMINCOMEFamily income > $195,000 and <= $215,000                    0.2102978
X1FAMINCOMEFamily income > $215,000 and <= $235,000                    0.1432016
X1FAMINCOMEFamily income > $235,000                                    0.1595624
X3TCREDAPIB                                                            0.0292806
X1CONTROLCatholic or other private                                     0.0861247
                                                                      Std. Error
(Intercept)                                                            0.0618736
X1STU30OCC2Management Occupations                                      0.0575649
X1STU30OCC2Business and Financial Operations Occupations               0.0717997
X1STU30OCC2Computer and Mathematical Occupations                       0.0645507
X1STU30OCC2Architecture and Engineering Occupations                    0.0374192
X1STU30OCC2Life, Physical, and Social Science Occupations              0.0369491
X1STU30OCC2Community and Social Services Occupations                   0.0866033
X1STU30OCC2Legal Occupations                                           0.0430488
X1STU30OCC2Education, Training, and Library Occupations                0.0419590
X1STU30OCC2Arts, Design, Entertainment, Sports, and Media Occupations  0.0290267
X1STU30OCC2Healthcare Practitioners and Technical Occupations          0.0236654
X1STU30OCC2Healthcare Support Occupations                              0.2132309
X1STU30OCC2Protective Service Occupations                              0.0596469
X1STU30OCC2Food Preparation and Serving Related Occupations            0.0864662
X1STU30OCC2Personal Care and Service Occupations                       0.0832071
X1STU30OCC2Sales and Related Occupations                               0.1296512
X1STU30OCC2Farming, Fishing, and Forestry Occupations                  0.2244406
X1STU30OCC2Construction and Extraction Occupations                     0.1517391
X1STU30OCC2Installation, Maintenance, and Repair Occupations           0.1039421
X1STU30OCC2Production Occupations                                      0.1767864
X1STU30OCC2Transportation and Material Moving Occupations              0.1132055
X1STU30OCC2Military Specific Occupations                               0.0686630
X3TGPAACAD                                                             0.0136806
X4ENTRYMAJ23Computer and information sciences                          0.0569549
X4ENTRYMAJ23Engineering and engineering technology                     0.0469181
X4ENTRYMAJ23Biological and physical science, science tech              0.0450795
X4ENTRYMAJ23Mathematics                                                0.0965082
X4ENTRYMAJ23Agriculture and natural resources                          0.0708381
X4ENTRYMAJ23General studies and other                                  0.0700379
X4ENTRYMAJ23Social sciences                                            0.0589234
X4ENTRYMAJ23Psychology                                                 0.0548070
X4ENTRYMAJ23Humanities                                                 0.0522431
X4ENTRYMAJ23History                                                    0.0951975
X4ENTRYMAJ23Personal and consumer services                             0.0608408
X4ENTRYMAJ23Manufacturing, construction, repair, transportation        0.0726747
X4ENTRYMAJ23Military technology and protective services                0.0581589
X4ENTRYMAJ23Health care fields                                         0.0424604
X4ENTRYMAJ23Business                                                   0.0434976
X4ENTRYMAJ23Education                                                  0.0506218
X4ENTRYMAJ23Architecture                                               0.1211585
X4ENTRYMAJ23Communications                                             0.0602309
X4ENTRYMAJ23Public administration and human services                   0.0927785
X4ENTRYMAJ23Design and applied arts                                    0.0832168
X4ENTRYMAJ23Law and legal studies                                      0.1223645
X4ENTRYMAJ23Theology and religious vocations                           0.1661350
X1FAMINCOMEFamily income > $15,000 and <= $35,000                      0.0424455
X1FAMINCOMEFamily income > $35,000 and <= $55,000                      0.0416326
X1FAMINCOMEFamily income > $55,000 and <= $75,000                      0.0416099
X1FAMINCOMEFamily income > $75,000 and <= $95,000                      0.0425920
X1FAMINCOMEFamily income > $95,000 and <= $115,000                     0.0438472
X1FAMINCOMEFamily income > $115,000 and <= $135,000                    0.0467359
X1FAMINCOMEFamily income > $135,000 and <= $155,000                    0.0492487
X1FAMINCOMEFamily income > $155,000 and <=$175,000                     0.0596338
X1FAMINCOMEFamily income > $175,000 and <= $195,000                    0.0714790
X1FAMINCOMEFamily income > $195,000 and <= $215,000                    0.0635681
X1FAMINCOMEFamily income > $215,000 and <= $235,000                    0.0904840
X1FAMINCOMEFamily income > $235,000                                    0.0503627
X3TCREDAPIB                                                            0.0034555
X1CONTROLCatholic or other private                                     0.0199546
                                                                      t value
(Intercept)                                                             7.340
X1STU30OCC2Management Occupations                                       0.266
X1STU30OCC2Business and Financial Operations Occupations                1.090
X1STU30OCC2Computer and Mathematical Occupations                       -0.574
X1STU30OCC2Architecture and Engineering Occupations                    -1.564
X1STU30OCC2Life, Physical, and Social Science Occupations              -0.825
X1STU30OCC2Community and Social Services Occupations                    1.608
X1STU30OCC2Legal Occupations                                           -1.714
X1STU30OCC2Education, Training, and Library Occupations                 1.598
X1STU30OCC2Arts, Design, Entertainment, Sports, and Media Occupations  -0.175
X1STU30OCC2Healthcare Practitioners and Technical Occupations          -1.280
X1STU30OCC2Healthcare Support Occupations                               0.408
X1STU30OCC2Protective Service Occupations                              -0.880
X1STU30OCC2Food Preparation and Serving Related Occupations            -2.725
X1STU30OCC2Personal Care and Service Occupations                        1.181
X1STU30OCC2Sales and Related Occupations                                0.335
X1STU30OCC2Farming, Fishing, and Forestry Occupations                   0.522
X1STU30OCC2Construction and Extraction Occupations                      0.465
X1STU30OCC2Installation, Maintenance, and Repair Occupations            1.221
X1STU30OCC2Production Occupations                                       0.845
X1STU30OCC2Transportation and Material Moving Occupations               1.123
X1STU30OCC2Military Specific Occupations                               -2.425
X3TGPAACAD                                                             49.757
X4ENTRYMAJ23Computer and information sciences                          -0.072
X4ENTRYMAJ23Engineering and engineering technology                      0.006
X4ENTRYMAJ23Biological and physical science, science tech               1.786
X4ENTRYMAJ23Mathematics                                                 0.756
X4ENTRYMAJ23Agriculture and natural resources                           2.082
X4ENTRYMAJ23General studies and other                                   2.141
X4ENTRYMAJ23Social sciences                                             2.865
X4ENTRYMAJ23Psychology                                                  2.513
X4ENTRYMAJ23Humanities                                                  4.991
X4ENTRYMAJ23History                                                     1.550
X4ENTRYMAJ23Personal and consumer services                              2.279
X4ENTRYMAJ23Manufacturing, construction, repair, transportation         5.968
X4ENTRYMAJ23Military technology and protective services                 2.549
X4ENTRYMAJ23Health care fields                                          3.747
X4ENTRYMAJ23Business                                                    2.747
X4ENTRYMAJ23Education                                                   4.533
X4ENTRYMAJ23Architecture                                                1.814
X4ENTRYMAJ23Communications                                              4.699
X4ENTRYMAJ23Public administration and human services                    1.801
X4ENTRYMAJ23Design and applied arts                                     3.025
X4ENTRYMAJ23Law and legal studies                                       1.903
X4ENTRYMAJ23Theology and religious vocations                            2.107
X1FAMINCOMEFamily income > $15,000 and <= $35,000                       0.229
X1FAMINCOMEFamily income > $35,000 and <= $55,000                       1.304
X1FAMINCOMEFamily income > $55,000 and <= $75,000                       2.550
X1FAMINCOMEFamily income > $75,000 and <= $95,000                       1.904
X1FAMINCOMEFamily income > $95,000 and <= $115,000                      3.437
X1FAMINCOMEFamily income > $115,000 and <= $135,000                     3.653
X1FAMINCOMEFamily income > $135,000 and <= $155,000                     2.563
X1FAMINCOMEFamily income > $155,000 and <=$175,000                      1.597
X1FAMINCOMEFamily income > $175,000 and <= $195,000                     2.523
X1FAMINCOMEFamily income > $195,000 and <= $215,000                     3.308
X1FAMINCOMEFamily income > $215,000 and <= $235,000                     1.583
X1FAMINCOMEFamily income > $235,000                                     3.168
X3TCREDAPIB                                                             8.474
X1CONTROLCatholic or other private                                      4.316
                                                                      Pr(>|t|)
(Intercept)                                                           2.37e-13
X1STU30OCC2Management Occupations                                     0.790004
X1STU30OCC2Business and Financial Operations Occupations              0.275615
X1STU30OCC2Computer and Mathematical Occupations                      0.566241
X1STU30OCC2Architecture and Engineering Occupations                   0.117775
X1STU30OCC2Life, Physical, and Social Science Occupations             0.409157
X1STU30OCC2Community and Social Services Occupations                  0.107820
X1STU30OCC2Legal Occupations                                          0.086646
X1STU30OCC2Education, Training, and Library Occupations               0.110117
X1STU30OCC2Arts, Design, Entertainment, Sports, and Media Occupations 0.861432
X1STU30OCC2Healthcare Practitioners and Technical Occupations         0.200493
X1STU30OCC2Healthcare Support Occupations                             0.683603
X1STU30OCC2Protective Service Occupations                             0.379042
X1STU30OCC2Food Preparation and Serving Related Occupations           0.006442
X1STU30OCC2Personal Care and Service Occupations                      0.237801
X1STU30OCC2Sales and Related Occupations                              0.737649
X1STU30OCC2Farming, Fishing, and Forestry Occupations                 0.601633
X1STU30OCC2Construction and Extraction Occupations                    0.641997
X1STU30OCC2Installation, Maintenance, and Repair Occupations          0.222111
X1STU30OCC2Production Occupations                                     0.398059
X1STU30OCC2Transportation and Material Moving Occupations             0.261353
X1STU30OCC2Military Specific Occupations                              0.015321
X3TGPAACAD                                                             < 2e-16
X4ENTRYMAJ23Computer and information sciences                         0.942325
X4ENTRYMAJ23Engineering and engineering technology                    0.995420
X4ENTRYMAJ23Biological and physical science, science tech             0.074162
X4ENTRYMAJ23Mathematics                                               0.449940
X4ENTRYMAJ23Agriculture and natural resources                         0.037401
X4ENTRYMAJ23General studies and other                                 0.032336
X4ENTRYMAJ23Social sciences                                           0.004183
X4ENTRYMAJ23Psychology                                                0.011992
X4ENTRYMAJ23Humanities                                                6.15e-07
X4ENTRYMAJ23History                                                   0.121110
X4ENTRYMAJ23Personal and consumer services                            0.022713
X4ENTRYMAJ23Manufacturing, construction, repair, transportation       2.51e-09
X4ENTRYMAJ23Military technology and protective services               0.010831
X4ENTRYMAJ23Health care fields                                        0.000180
X4ENTRYMAJ23Business                                                  0.006028
X4ENTRYMAJ23Education                                                 5.91e-06
X4ENTRYMAJ23Architecture                                              0.069653
X4ENTRYMAJ23Communications                                            2.66e-06
X4ENTRYMAJ23Public administration and human services                  0.071769
X4ENTRYMAJ23Design and applied arts                                   0.002498
X4ENTRYMAJ23Law and legal studies                                     0.057115
X4ENTRYMAJ23Theology and religious vocations                          0.035193
X1FAMINCOMEFamily income > $15,000 and <= $35,000                     0.818947
X1FAMINCOMEFamily income > $35,000 and <= $55,000                     0.192342
X1FAMINCOMEFamily income > $55,000 and <= $75,000                     0.010781
X1FAMINCOMEFamily income > $75,000 and <= $95,000                     0.056891
X1FAMINCOMEFamily income > $95,000 and <= $115,000                    0.000591
X1FAMINCOMEFamily income > $115,000 and <= $135,000                   0.000261
X1FAMINCOMEFamily income > $135,000 and <= $155,000                   0.010412
X1FAMINCOMEFamily income > $155,000 and <=$175,000                    0.110231
X1FAMINCOMEFamily income > $175,000 and <= $195,000                   0.011657
X1FAMINCOMEFamily income > $195,000 and <= $215,000                   0.000943
X1FAMINCOMEFamily income > $215,000 and <= $235,000                   0.113552
X1FAMINCOMEFamily income > $235,000                                   0.001540
X3TCREDAPIB                                                            < 2e-16
X1CONTROLCatholic or other private                                    1.61e-05
                                                                         
(Intercept)                                                           ***
X1STU30OCC2Management Occupations                                        
X1STU30OCC2Business and Financial Operations Occupations                 
X1STU30OCC2Computer and Mathematical Occupations                         
X1STU30OCC2Architecture and Engineering Occupations                      
X1STU30OCC2Life, Physical, and Social Science Occupations                
X1STU30OCC2Community and Social Services Occupations                     
X1STU30OCC2Legal Occupations                                          .  
X1STU30OCC2Education, Training, and Library Occupations                  
X1STU30OCC2Arts, Design, Entertainment, Sports, and Media Occupations    
X1STU30OCC2Healthcare Practitioners and Technical Occupations            
X1STU30OCC2Healthcare Support Occupations                                
X1STU30OCC2Protective Service Occupations                                
X1STU30OCC2Food Preparation and Serving Related Occupations           ** 
X1STU30OCC2Personal Care and Service Occupations                         
X1STU30OCC2Sales and Related Occupations                                 
X1STU30OCC2Farming, Fishing, and Forestry Occupations                    
X1STU30OCC2Construction and Extraction Occupations                       
X1STU30OCC2Installation, Maintenance, and Repair Occupations             
X1STU30OCC2Production Occupations                                        
X1STU30OCC2Transportation and Material Moving Occupations                
X1STU30OCC2Military Specific Occupations                              *  
X3TGPAACAD                                                            ***
X4ENTRYMAJ23Computer and information sciences                            
X4ENTRYMAJ23Engineering and engineering technology                       
X4ENTRYMAJ23Biological and physical science, science tech             .  
X4ENTRYMAJ23Mathematics                                                  
X4ENTRYMAJ23Agriculture and natural resources                         *  
X4ENTRYMAJ23General studies and other                                 *  
X4ENTRYMAJ23Social sciences                                           ** 
X4ENTRYMAJ23Psychology                                                *  
X4ENTRYMAJ23Humanities                                                ***
X4ENTRYMAJ23History                                                      
X4ENTRYMAJ23Personal and consumer services                            *  
X4ENTRYMAJ23Manufacturing, construction, repair, transportation       ***
X4ENTRYMAJ23Military technology and protective services               *  
X4ENTRYMAJ23Health care fields                                        ***
X4ENTRYMAJ23Business                                                  ** 
X4ENTRYMAJ23Education                                                 ***
X4ENTRYMAJ23Architecture                                              .  
X4ENTRYMAJ23Communications                                            ***
X4ENTRYMAJ23Public administration and human services                  .  
X4ENTRYMAJ23Design and applied arts                                   ** 
X4ENTRYMAJ23Law and legal studies                                     .  
X4ENTRYMAJ23Theology and religious vocations                          *  
X1FAMINCOMEFamily income > $15,000 and <= $35,000                        
X1FAMINCOMEFamily income > $35,000 and <= $55,000                        
X1FAMINCOMEFamily income > $55,000 and <= $75,000                     *  
X1FAMINCOMEFamily income > $75,000 and <= $95,000                     .  
X1FAMINCOMEFamily income > $95,000 and <= $115,000                    ***
X1FAMINCOMEFamily income > $115,000 and <= $135,000                   ***
X1FAMINCOMEFamily income > $135,000 and <= $155,000                   *  
X1FAMINCOMEFamily income > $155,000 and <=$175,000                       
X1FAMINCOMEFamily income > $175,000 and <= $195,000                   *  
X1FAMINCOMEFamily income > $195,000 and <= $215,000                   ***
X1FAMINCOMEFamily income > $215,000 and <= $235,000                      
X1FAMINCOMEFamily income > $235,000                                   ** 
X3TCREDAPIB                                                           ***
X1CONTROLCatholic or other private                                    ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.7035 on 7290 degrees of freedom
Multiple R-squared:  0.3613,    Adjusted R-squared:  0.3562 
F-statistic:  71.1 on 58 and 7290 DF,  p-value: < 2.2e-16

Diagnostics

Constant Variance

  • Breusch-Pagan test yields a p-value < 0.0001.

  • Because the response variable is bound.

Diagnostics

Normality

Remedial Measures

  • Need to address non-constant variance first, and then recheck normality assumption

  • Try Box-Cox transformation

  • Weighted Least Squares

  • Recheck model diagnostics.

Try Box-Cox Transformation

Need to get rid of all 0.0 GPAs


Call:
lm(formula = log(X5GPAALL) ~ X1STU30OCC2 + X3TGPAACAD + X4ENTRYMAJ23 + 
    X1FAMINCOME + X3TCREDAPIB + X1CONTROL, data = MLR_all_no_0)

Coefficients:
                                                          (Intercept)  
                                                            0.0109720  
                                    X1STU30OCC2Management Occupations  
                                                            0.0093697  
             X1STU30OCC2Business and Financial Operations Occupations  
                                                            0.0510748  
                     X1STU30OCC2Computer and Mathematical Occupations  
                                                           -0.0217388  
                  X1STU30OCC2Architecture and Engineering Occupations  
                                                           -0.0244767  
            X1STU30OCC2Life, Physical, and Social Science Occupations  
                                                           -0.0164916  
                 X1STU30OCC2Community and Social Services Occupations  
                                                            0.0460886  
                                         X1STU30OCC2Legal Occupations  
                                                           -0.0356596  
              X1STU30OCC2Education, Training, and Library Occupations  
                                                            0.0126841  
X1STU30OCC2Arts, Design, Entertainment, Sports, and Media Occupations  
                                                           -0.0155888  
        X1STU30OCC2Healthcare Practitioners and Technical Occupations  
                                                           -0.0150275  
                            X1STU30OCC2Healthcare Support Occupations  
                                                            0.0250619  
                            X1STU30OCC2Protective Service Occupations  
                                                           -0.0278352  
          X1STU30OCC2Food Preparation and Serving Related Occupations  
                                                           -0.1065543  
                     X1STU30OCC2Personal Care and Service Occupations  
                                                            0.0537492  
                             X1STU30OCC2Sales and Related Occupations  
                                                           -0.0283844  
                X1STU30OCC2Farming, Fishing, and Forestry Occupations  
                                                            0.0546602  
                   X1STU30OCC2Construction and Extraction Occupations  
                                                           -0.0629834  
         X1STU30OCC2Installation, Maintenance, and Repair Occupations  
                                                            0.0007898  
                                    X1STU30OCC2Production Occupations  
                                                            0.0754804  
            X1STU30OCC2Transportation and Material Moving Occupations  
                                                            0.0533044  
                             X1STU30OCC2Military Specific Occupations  
                                                           -0.0252304  
                                                           X3TGPAACAD  
                                                            0.2797622  
                        X4ENTRYMAJ23Computer and information sciences  
                                                            0.0107104  
                   X4ENTRYMAJ23Engineering and engineering technology  
                                                            0.0077480  
            X4ENTRYMAJ23Biological and physical science, science tech  
                                                            0.0411161  
                                              X4ENTRYMAJ23Mathematics  
                                                            0.0503698  
                        X4ENTRYMAJ23Agriculture and natural resources  
                                                            0.0761258  
                                X4ENTRYMAJ23General studies and other  
                                                            0.0600307  
                                          X4ENTRYMAJ23Social sciences  
                                                            0.0802116  
                                               X4ENTRYMAJ23Psychology  
                                                            0.0707090  
                                               X4ENTRYMAJ23Humanities  
                                                            0.1099460  
                                                  X4ENTRYMAJ23History  
                                                            0.0569046  
                           X4ENTRYMAJ23Personal and consumer services  
                                                            0.0562186  
      X4ENTRYMAJ23Manufacturing, construction, repair, transportation  
                                                            0.1867279  
              X4ENTRYMAJ23Military technology and protective services  
                                                            0.0872411  
                                       X4ENTRYMAJ23Health care fields  
                                                            0.0708053  
                                                 X4ENTRYMAJ23Business  
                                                            0.0528408  
                                                X4ENTRYMAJ23Education  
                                                            0.1059681  
                                             X4ENTRYMAJ23Architecture  
                                                            0.1305971  
                                           X4ENTRYMAJ23Communications  
                                                            0.1173337  
                 X4ENTRYMAJ23Public administration and human services  
                                                            0.0597354  
                                  X4ENTRYMAJ23Design and applied arts  
                                                            0.1412065  
                                    X4ENTRYMAJ23Law and legal studies  
                                                            0.1224035  
                         X4ENTRYMAJ23Theology and religious vocations  
                                                            0.1383546  
                    X1FAMINCOMEFamily income > $15,000 and <= $35,000  
                                                            0.0045253  
                    X1FAMINCOMEFamily income > $35,000 and <= $55,000  
                                                            0.0336240  
                    X1FAMINCOMEFamily income > $55,000 and <= $75,000  
                                                            0.0493288  
                    X1FAMINCOMEFamily income > $75,000 and <= $95,000  
                                                            0.0286809  
                   X1FAMINCOMEFamily income > $95,000 and <= $115,000  
                                                            0.0627845  
                  X1FAMINCOMEFamily income > $115,000 and <= $135,000  
                                                            0.0732202  
                  X1FAMINCOMEFamily income > $135,000 and <= $155,000  
                                                            0.0575691  
                   X1FAMINCOMEFamily income > $155,000 and <=$175,000  
                                                            0.0393550  
                  X1FAMINCOMEFamily income > $175,000 and <= $195,000  
                                                            0.0870046  
                  X1FAMINCOMEFamily income > $195,000 and <= $215,000  
                                                            0.0959278  
                  X1FAMINCOMEFamily income > $215,000 and <= $235,000  
                                                            0.0775971  
                                  X1FAMINCOMEFamily income > $235,000  
                                                            0.0690836  
                                                          X3TCREDAPIB  
                                                            0.0106625  
                                   X1CONTROLCatholic or other private  
                                                            0.0273573  

Box-Cox Residual Variance

Still a pattern

Weighted Least Squares on Full Model

Can’t reach coefficient convergence.

Make Predictor “Don’t Know” vs. “Know” Future Occupation


Call:
lm(formula = X5GPAALL ~ career + X3TGPAACAD, data = MLR_all)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.1704 -0.3517  0.1174  0.4483  2.9471 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.58715    0.04001   14.67   <2e-16 ***
career      -0.01878    0.01859   -1.01    0.313    
X3TGPAACAD   0.73808    0.01212   60.92   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.7148 on 7346 degrees of freedom
Multiple R-squared:  0.3356,    Adjusted R-squared:  0.3355 
F-statistic:  1856 on 2 and 7346 DF,  p-value: < 2.2e-16

0-1 Career Residual Variance

Still a pattern.